Correlated equilibrium implementation: Navigating toward social optima with learning dynamics

2025-06-04

AI Summary

Traditional mechanism design relies on agents’ strong strategic reasoning capabilities, limiting applicability under bounded rationality. Method: We propose a correlated-equilibrium-based full implementation mechanism tailored for boundedly rational agents, achieving robust realization of Maskin-monotonic social choice functions—without resorting to integer games or modular arithmetic. Our approach employs a simple finite mechanism coupled with adaptive learning dynamics (e.g., regret matching), enabling agents to converge to socially optimal outcomes using only local feedback. Contribution/Results: (1) We extend full implementation via correlated equilibria to bounded-rational settings for the first time; (2) We provide theoretical guarantees that agents—despite lacking knowledge of others’ preferences or the equilibrium structure—uniquely converge to the target outcome via simple, decentralized learning; (3) Bilateral trade simulations confirm the mechanism’s robustness to cognitive constraints and its practical feasibility.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Implementation theory has made significant advances in characterizing which social choice functions can be implemented in Nash equilibrium, but these results typically assume sophisticated strategic reasoning by agents. However, evidence exists to show that agents frequently cannot perform such reasoning. In this paper, we present a finite mechanism which fully implements Maskin-monotonic social choice functions as the outcome of the unique correlated equilibrium of the induced game. Due to the results in Hart and MasColell (2000), this yields that even when agents use a simple adaptive heuristic like regret minimization rather than computing equilibrium strategies, the designer can expect to implement the SCF correctly. We demonstrate the mechanism's effectiveness through simulations in a bilateral trade environment, where agents using regret matching converge to the desired outcomes despite having no knowledge of others' preferences or the equilibrium structure. The mechanism does not use integer games or modulo games.

Problem

• Implementing social choice functions via correlated equilibrium
• Using adaptive heuristics instead of complex strategic reasoning
• Achieving desired outcomes in bilateral trade with regret matching

Innovation

• Finite mechanism implements Maskin-monotonic functions
• Uses correlated equilibrium with regret minimization
• No integer or modulo games required